1 Introduction

This paper contains estimates for the effective reproduction number \(R_{t,m}\) over time \(t\) in various countries \(m\) of the world. This is done using the methodology as described in [1]. These have been implemented in R using EpiEstim package [2] which is what is used here. The methodology and assumptions are described in more detail here.

This paper and it’s results should be updated roughly daily and is available online.

As this paper is updated over time this section will summarise significant changes. The code producing this paper is tracked using Git. The Git commit hash for this project at the time of generating this paper was 87b8bf86ada0300fd651f355dad57b03e6b15b4d.

2 Data

Data are downloaded from [3]. Minor formatting is applied to get the data ready for further processing.

3 Basic Exploration

Below we plot cumulative case count on a log scale by continent. Note that “Other” relates to ships.

Reported Cases by Continent

Reported Cases by Continent

Below we plot the cumulative deaths by country on a log scale:

Reported Deaths by Continent

Reported Deaths by Continent

4 Method & Assumptions

The methodology is described in detail here.

Countries with populations of less than 500 000 are excluded.

5 Results

5.1 Current \(R_{t,m}\) estimates by country

Below current (last weekly) \(R_{t,m}\) estimates are plotted on a world map.

5.1.0.1 Cases

5.1.1 Deaths

5.2 Top 10 countries

Below we show various extremes of \(R_{t,m}\) where counts (deaths or cases) exceed 50 in the last week.

5.2.1 Lowest \(R_{t,m}\) based on deaths

Country Estimated Type Count (Last Week) Week Ending R - Lower CI R - Mean R - Uppper CI
Philippines deaths 116 2021-01-08 0.6 0.7 0.9
Pakistan deaths 340 2021-01-08 0.7 0.8 0.9
Iran deaths 681 2021-01-08 0.7 0.8 0.9
Poland deaths 1,618 2021-01-08 0.8 0.8 0.9
Belgium deaths 411 2021-01-08 0.8 0.8 0.9
Turkey deaths 1,357 2021-01-08 0.8 0.8 0.9
Azerbaijan deaths 199 2021-01-08 0.7 0.8 1.0
Moldova deaths 118 2021-01-08 0.7 0.9 1.0
Croatia deaths 343 2021-01-08 0.8 0.9 1.0
North Macedonia deaths 82 2021-01-08 0.7 0.9 1.1

5.2.2 Lowest \(R_{t,m}\) based on cases

Country Estimated Type Count (Last Week) Week Ending R - Lower CI R - Mean R - Uppper CI
Mali cases 309 2021-01-08 0.5 0.5 0.6
Uzbekistan cases 303 2021-01-08 0.5 0.6 0.7
Armenia cases 1,677 2021-01-08 0.6 0.7 0.7
Mauritania cases 771 2021-01-08 0.6 0.7 0.7
Honduras cases 2,583 2021-01-08 0.6 0.7 0.7
Azerbaijan cases 4,376 2021-01-08 0.6 0.7 0.8
Bhutan cases 78 2021-01-08 0.6 0.7 0.9
Croatia cases 5,939 2021-01-08 0.7 0.7 0.8
Moldova cases 3,411 2021-01-08 0.7 0.7 0.8
North Macedonia cases 1,851 2021-01-08 0.7 0.7 0.8

5.2.3 Highest \(R_{t,m}\) based on deaths

Country Estimated Type Count (Last Week) Week Ending R - Lower CI R - Mean R - Uppper CI
Zambia deaths 51 2021-01-08 2.3 3.5 5.2
Zimbabwe deaths 99 2021-01-08 1.9 2.6 3.4
Guatemala deaths 152 2021-01-08 1.8 2.2 2.6
Malaysia deaths 63 2021-01-08 1.2 1.6 2.1
Sweden deaths 706 2021-01-08 1.5 1.6 1.8
Bolivia deaths 153 2021-01-08 1.3 1.5 1.8
Ecuador deaths 114 2021-01-08 1.2 1.5 1.9
El Salvador deaths 71 2021-01-08 1.1 1.5 1.9
Ireland deaths 79 2021-01-08 1.1 1.4 1.7
United Kingdom deaths 5,728 2021-01-08 1.3 1.3 1.4

5.2.4 Highest \(R_{t,m}\) based on cases

Country Estimated Type Count (Last Week) Week Ending R - Lower CI R - Mean R - Uppper CI
Lesotho cases 1,964 2021-01-08 3.5 4.6 5.2
Ireland cases 42,352 2021-01-08 2.0 2.5 3.1
Malawi cases 1,241 2021-01-08 2.0 2.5 3.0
Zimbabwe cases 5,576 2021-01-08 1.9 2.4 3.1
Zambia cases 4,329 2021-01-08 1.9 2.3 2.6
Cape Verde cases 365 2021-01-08 1.6 1.8 2.0
Mozambique cases 1,688 2021-01-08 1.6 1.7 1.9
Burundi cases 63 2021-01-08 1.2 1.7 2.2
Afghanistan cases 1,806 2021-01-08 1.3 1.6 2.1
Togo cases 232 2021-01-08 1.4 1.6 1.9

5.3 Risk Quadrants

The plots below show weekly cases (or deaths) on the X-axis and the reproduction number on the Y-axis. By dividing this into 4 quadrants we can identify countries with high cases and high reproduction numbers, or high cases and low reproduction numbers etc.

Values where the reproduction number exceeds 3 are plotted at 3.

5.3.1 Cases

Risk Quadrants - Cases

5.3.2 Deaths

Risk Quadrants - Deaths

5.4 Country Plots by Continent

Below we plot results for each country/province in a list. Values larger than 3 are plotted at 3.

5.4.1 Africa

5.4.1.1 Algeria

5.4.1.2 Angola

5.4.1.3 Benin

5.4.1.4 Botswana

5.4.1.5 Burkina Faso

5.4.1.6 Burundi

5.4.1.7 Cameroon

5.4.1.8 Cape Verde

5.4.1.9 Central African Republic

5.4.1.10 Chad

5.4.1.11 Comoros

5.4.1.12 Congo

5.4.1.13 Cote d’Ivoire

5.4.1.14 Democratic Republic of Congo

5.4.1.15 Djibouti

5.4.1.16 Egypt

5.4.1.17 Equatorial Guinea

5.4.1.18 Eritrea

5.4.1.19 Eswatini

5.4.1.20 Ethiopia

5.4.1.21 Gabon

5.4.1.22 Gambia

5.4.1.23 Ghana

5.4.1.24 Guinea

5.4.1.25 Guinea-Bissau

5.4.1.26 Kenya

5.4.1.27 Lesotho

5.4.1.28 Liberia

5.4.1.29 Libya

5.4.1.30 Madagascar

5.4.1.31 Malawi

5.4.1.32 Mali

5.4.1.33 Mauritania

5.4.1.34 Mauritius

5.4.1.35 Morocco

5.4.1.36 Mozambique

5.4.1.37 Namibia

5.4.1.38 Niger

5.4.1.39 Nigeria

5.4.1.40 Rwanda

5.4.1.41 Senegal

5.4.1.42 Sierra Leone

5.4.1.43 Somalia

5.4.1.44 South Africa

5.4.1.45 South Sudan

5.4.1.46 Sudan

5.4.1.47 Togo

5.4.1.48 Tunisia

5.4.1.49 Uganda

5.4.1.50 Zambia

5.4.1.51 Zimbabwe

5.4.2 Asia

5.4.2.1 Afghanistan

5.4.2.2 Armenia

5.4.2.3 Azerbaijan

5.4.2.4 Bahrain

5.4.2.5 Bangladesh

5.4.2.6 Bhutan

5.4.2.7 Cambodia

5.4.2.8 China

5.4.2.9 Georgia

5.4.2.10 India

5.4.2.11 Indonesia

5.4.2.12 Iran

5.4.2.13 Iraq

5.4.2.14 Israel

5.4.2.15 Japan

5.4.2.16 Jordan

5.4.2.17 Kazakhstan

5.4.2.18 Kuwait

5.4.2.19 Kyrgyzstan

5.4.2.20 Lebanon

5.4.2.21 Malaysia

5.4.2.22 Maldives

5.4.2.23 Mongolia

5.4.2.24 Myanmar

5.4.2.25 Nepal

5.4.2.26 Oman

5.4.2.27 Pakistan

5.4.2.28 Palestine

5.4.2.29 Philippines

5.4.2.30 Qatar

5.4.2.31 Saudi Arabia

5.4.2.32 Singapore

5.4.2.33 South Korea

5.4.2.34 Sri Lanka

5.4.2.35 Syria

5.4.2.36 Taiwan

5.4.2.37 Tajikistan

5.4.2.38 Thailand

5.4.2.39 Turkey

5.4.2.40 United Arab Emirates

5.4.2.41 Uzbekistan

5.4.2.42 Vietnam

5.4.2.43 Yemen

5.4.3 Europe

5.4.3.1 Albania

5.4.3.2 Austria

5.4.3.3 Belarus

5.4.3.4 Belgium

5.4.3.5 Bosnia and Herzegovina

5.4.3.6 Bulgaria

5.4.3.7 Croatia

5.4.3.8 Cyprus

5.4.3.9 Czechia

5.4.3.10 Denmark

5.4.3.11 Estonia

5.4.3.12 Finland

5.4.3.13 France

5.4.3.14 Germany

5.4.3.15 Greece

5.4.3.16 Hungary

5.4.3.17 Ireland

5.4.3.18 Italy

5.4.3.19 Kosovo

5.4.3.20 Latvia

5.4.3.21 Lithuania

5.4.3.22 Luxembourg

5.4.3.23 Moldova

5.4.3.24 Montenegro

5.4.3.25 Netherlands

5.4.3.26 North Macedonia

5.4.3.27 Norway

5.4.3.28 Poland

5.4.3.29 Portugal

5.4.3.30 Romania

5.4.3.31 Russia

5.4.3.32 Serbia

5.4.3.33 Slovakia

5.4.3.34 Slovenia

5.4.3.35 Spain

5.4.3.36 Sweden

5.4.3.37 Switzerland

5.4.3.38 Ukraine

5.4.3.39 United Kingdom

5.4.4 North America

5.4.4.1 Canada

5.4.4.2 Costa Rica

5.4.4.3 Cuba

5.4.4.4 Dominican Republic

5.4.4.5 El Salvador

5.4.4.6 Guatemala

5.4.4.7 Haiti

5.4.4.8 Honduras

5.4.4.9 Jamaica

5.4.4.10 Mexico

5.4.4.11 Nicaragua

5.4.4.12 Panama

5.4.4.13 Trinidad and Tobago

5.4.4.14 United States

5.4.5 Oceania

5.4.5.1 Australia

5.4.5.2 New Zealand

5.4.5.3 Papua New Guinea

5.4.6 South America

5.4.6.1 Argentina

5.4.6.2 Bolivia

5.4.6.3 Brazil

5.4.6.4 Chile

5.4.6.5 Colombia

5.4.6.6 Ecuador

5.4.6.7 Guyana

5.4.6.8 Paraguay

5.4.6.9 Peru

5.4.6.10 Suriname

5.4.6.11 Uruguay

5.4.6.12 Venezuela

5.5 Detailed Output

Detailed output for all countries are saved to a comma-separated value file. The file can be found here.

6 Discussion

Limitation of this method to estimate \(R_{t,m}\) are noted in [1]

  • It’s sensitive to changes in transmissibility, changes in contact patterns, depletion of the susceptible population and control measures.
  • It relies on an assumed generation interval assumptions.
  • The size of the time window can affect the volatility of results.
  • Results are time lagged with regards to true infection, more so in the case of the use of deaths.
  • It’s sensitive to changes in case (or death) detection.
  • The generation interval may change over time.

Further to the above the estimates are made under assumption that the cases and deaths are reported consistently over time. For cases this means that testing needs to be at similar levels and reported with similar lag. Should these change rapidly over an interval of a few weeks the above estimates of the effective reproduction numbers would be biased. For example a rapid expansion of testing over the last 3 weeks would results in overestimating recent effective reproduction numbers. Similarly any changes in reporting (over time and underreporting) of deaths would also bias estimates of the reproduction number estimated using deaths.

Estimates for the reproduction number are plotted in time period in which the relevant measure is recorded. Though in reality the infections giving rise to those estimates would have occurred roughly between a week to 4 weeks earlier depending on whether it was cases or deaths. These figures have not been shifted back.

Despite these limitation we believe the ease of calculation of this method and the ability to use multiple sources makes it useful as a monitoring tool.

7 Author

This report was prepared by Louis Rossouw. Please get in contact with Louis Rossouw if you have comments or wish to receive this regularly.

Louis Rossouw
Head of Research & Analytics
Gen Re | Life/Health Canada, South Africa, Australia, NZ, UK & Ireland
Email: LRossouw@GenRe.com Mobile: +27 71 355 2550

The views in this document represents that of the author and may not represent those of Gen Re. Also note that given the significant uncertainty involved with the parameters, data and methodology care should be taken with these numbers and any use of these numbers.

References

[1] A. Cori, N. M. Ferguson, C. Fraser, and S. Cauchemez, “A new framework and software to estimate time-varying reproduction numbers during epidemics,” American Journal of Epidemiology, vol. 178, no. 9, pp. 1505–1512, Sep. 2013, doi: 10.1093/aje/kwt133. [Online]. Available: https://doi.org/10.1093/aje/kwt133

[2] A. Cori, EpiEstim: A package to estimate time varying reproduction numbers from epidemic curves. 2013 [Online]. Available: https://CRAN.R-project.org/package=EpiEstim

[3] M. Roser, H. Ritchie, E. Ortiz-Ospina, and J. Hasell, “Coronavirus pandemic (COVID-19),” Our World in Data, 2020 [Online]. Available: https://ourworldindata.org/coronavirus. [Accessed: 17-Dec-2020]